Lattice Boltzmann simulation of droplet coalescence and transport in a fibrous filter

Understanding the principles of droplet coalescence and transport in fibrous filter media is a prerequisite for guiding the design of new filter media and optimizing their performance. In this work, we have developed a three-dimensional pore-scale numerical model for the coalescence filtration process in fibrous filter media with an improved virtual density scheme and an extended outflow boundary condition to successfully simulate both droplet capture and outflow processes in a multi-droplet system. We also conducted single-phase and two-phase residual saturation experiments to verify the validity of this model. Additionally, the effects of contact angle (θ = 48.3°–132.8°) and fiber diameter (df = 1–8 μm) were systematically investigated. The results show that the coalescence and transport modes of droplets in the fibrous filter media can be classified into four types: surface interception, random collision, liquid cluster, and liquid bridge. A phase diagram was subsequently constructed based on these modes, which illustrates the principles by which wettability and fiber diameter control the coalescence and transport behavior. Enhanced wettability promotes the spreading and adhesion of droplets on fibers, which facilitates the formation of liquid clusters and liquid bridges. This not only causes the filter saturation to rise continuously and increase the amplitude of its fluctuations, but also results in a significant rise in the pressure drop. When θ increases from 48.3° to 132.8°, the pressure drop decreases by 68.75%. The variation in fiber diameter influences droplet capture and secondary coalescence by regulating the porosity and specific surface area. Fine fibers tend to restrict the available space for droplet growth, whereas coarse fibers reduce the probability of droplet recapture and secondary coalescence. When df = 6 μm, the maximum droplet size at the outflow side is ∼70 μm. Consequently, for given operating conditions, the selection of filter media requires a balance between capture efficiency and coalescence performance.